Does anybody can help me how to create in Illustrator something like that pictureabove? I'm beginner in Illustrator ang I 've been trying to do that for a week. Sorry for language mistakes I'm not native English.

Follow Jacob's advice in the message above. Select your rectangles and from the Object menu choose Expand (or Expand Appearance which ever is available) and then use Ungroup to make a series of rectangles which can be moved seperately.